Yang–Mills–Higgs soliton dynamics in $2+1$ dimensions

Dimensional reduction of the self-dual Yang–Mills equation in $2+2$ dimensions produces an integrable Yang–Mills–Higgs–Bogomolnyi equation in $2+1$ dimensions. For the ${\mathrm SU}(1,1)$ gauge group, a t'Hooft-like ansatz is used to construct a monopole-like solution and an $N$-soliton-type solution, which describes both the static deformed monopoles and the exotic monopole dynamics including a transmutation. How the monopole solution results from the twistor formalism is shown. Multimonopole solutions are commented on.